Contracting cube#
In this demo we simulate a unit cube that is fixed at \(x = 0\) and free at \(x = 1\). We use a transversally isotropic material with fiber oriented in the \(x\)-direction.
import dolfin
try:
from dolfin_adjoint import (
Constant,
DirichletBC,
Expression,
UnitCubeMesh,
interpolate,
Mesh,
)
except ImportError:
from dolfin import (
Constant,
DirichletBC,
interpolate,
Expression,
UnitCubeMesh,
Mesh,
)
import pulse
from fenics_plotly import plot
pulse.iterate.logger.setLevel(10)
# Create mesh
N = 6
mesh = UnitCubeMesh(N, N, N)
# Create subdomains
class Free(dolfin.SubDomain):
def inside(self, x, on_boundary):
return x[0] > (1.0 - dolfin.DOLFIN_EPS) and on_boundary
class Fixed(dolfin.SubDomain):
def inside(self, x, on_boundary):
return x[0] < dolfin.DOLFIN_EPS and on_boundary
# Create a facet fuction in order to mark the subdomains
ffun = dolfin.MeshFunction("size_t", mesh, 2)
ffun.set_all(0)
# Mark the first subdomain with value 1
fixed = Fixed()
fixed_marker = 1
fixed.mark(ffun, fixed_marker)
# Mark the second subdomain with value 2
free = Free()
free_marker = 2
free.mark(ffun, free_marker)
# Create a cell function (but we are not using it)
cfun = dolfin.MeshFunction("size_t", mesh, 3)
cfun.set_all(0)
# Collect the functions containing the markers
marker_functions = pulse.MarkerFunctions(ffun=ffun, cfun=cfun)
# Create mictrotructure
V_f = dolfin.VectorFunctionSpace(mesh, "CG", 1)
# Fibers
f0 = interpolate(Expression(("1.0", "0.0", "0.0"), degree=1), V_f)
# Sheets
s0 = interpolate(Expression(("0.0", "1.0", "0.0"), degree=1), V_f)
# Fiber-sheet normal
n0 = interpolate(Expression(("0.0", "0.0", "1.0"), degree=1), V_f)
# Collect the mictrotructure
microstructure = pulse.Microstructure(f0=f0, s0=s0, n0=n0)
# Create the geometry
geometry = pulse.Geometry(
mesh=mesh,
marker_functions=marker_functions,
microstructure=microstructure,
)
# Use the default material parameters
material_parameters = pulse.HolzapfelOgden.default_parameters()
# Select model for active contraction
active_model = pulse.ActiveModels.active_strain
# active_model = "active_stress"
# Set the activation
activation = Constant(0.0)
# Create material
material = pulse.HolzapfelOgden(
active_model=active_model,
parameters=material_parameters,
activation=activation,
)
# Make Dirichlet boundary conditions
def dirichlet_bc(W):
V = W if W.sub(0).num_sub_spaces() == 0 else W.sub(0)
return DirichletBC(V, Constant((0.0, 0.0, 0.0)), fixed)
# Make Neumann boundary conditions
neumann_bc = pulse.NeumannBC(traction=Constant(0.0), marker=free_marker)
# Collect Boundary Conditions
bcs = pulse.BoundaryConditions(dirichlet=(dirichlet_bc,), neumann=(neumann_bc,))
# Create problem
problem = pulse.MechanicsProblem(geometry, material, bcs)
# Solve problem
pulse.iterate.iterate(problem, activation, 0.1)
2023-10-04 10:11:55,108 [1230] DEBUG pulse.iterate: Control: [0.0]
2023-10-04 10:11:55,110 [1230] DEBUG pulse.iterate: Target: [0.1]
2023-10-04 10:11:55,111 [1230] DEBUG pulse.iterate: Intial number of steps: 5 with step size 0.02
2023-10-04 10:11:55,113 [1230] INFO pulse.iterate: Iterating to target control (f_21)...
2023-10-04 10:11:55,114 [1230] INFO pulse.iterate: Current control: f_21 = 0.000
2023-10-04 10:11:55,114 [1230] INFO pulse.iterate: Target: 0.100
2023-10-04 10:11:55,116 [1230] DEBUG pulse.iterate: Check target reached: NO
2023-10-04 10:11:55,117 [1230] DEBUG pulse.iterate: Maximum difference: 1.000e-01
2023-10-04 10:11:55,119 [1230] DEBUG pulse.iterate: Try new control
2023-10-04 10:11:55,120 [1230] DEBUG pulse.iterate: Current control: 0.020
2023-10-04 10:11:55,268 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:11:55,268 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:11:55,270 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:11:55,271 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:11:55,271 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:11:55,272 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:11:55,272 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:11:55,273 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:11:55,274 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:11:55,274 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:11:55,275 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:11:56,505 [1230] DEBUG UFL_LEGACY: Blocks of each mode:
99 full
2023-10-04 10:11:56,762 [1230] DEBUG UFL_LEGACY: Blocks of each mode:
18 full
2023-10-04 10:13:22,892 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:13:22,893 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:13:22,895 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:13:22,895 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:13:22,896 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:13:22,897 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:13:22,897 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:13:22,898 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:13:22,898 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:13:22,899 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:13:22,899 [1230] INFO UFL_LEGACY: Adjusting missing element cell to tetrahedron.
2023-10-04 10:13:23,109 [1230] DEBUG UFL_LEGACY: Blocks of each mode:
10 full
2023-10-04 10:13:23,342 [1230] DEBUG UFL_LEGACY: Blocks of each mode:
3 full
2023-10-04 10:13:25,770 [1230] DEBUG pulse.iterate: Solver did not converge...
2023-10-04 10:13:25,772 [1230] DEBUG pulse.iterate:
NOT CONVERGING
2023-10-04 10:13:25,773 [1230] DEBUG pulse.iterate: Reduce control step
2023-10-04 10:13:25,773 [1230] DEBUG pulse.iterate: Assign old state
2023-10-04 10:13:25,779 [1230] DEBUG pulse.iterate: Check target reached: NO
2023-10-04 10:13:25,779 [1230] DEBUG pulse.iterate: Maximum difference: 1.000e-01
2023-10-04 10:13:25,781 [1230] DEBUG pulse.iterate: Try new control
2023-10-04 10:13:25,783 [1230] DEBUG pulse.iterate: Current control: 0.010
*** Warning: PETSc SNES solver diverged in 2 iterations with divergence reason DIVERGED_FNORM_NAN.
2023-10-04 10:13:29,288 [1230] DEBUG pulse.iterate:
SUCCESFULL STEP:
2023-10-04 10:13:29,289 [1230] DEBUG pulse.iterate: Check target reached: NO
2023-10-04 10:13:29,291 [1230] DEBUG pulse.iterate: Maximum difference: 9.000e-02
2023-10-04 10:13:29,292 [1230] DEBUG pulse.iterate: Check target reached: NO
2023-10-04 10:13:29,292 [1230] DEBUG pulse.iterate: Maximum difference: 9.000e-02
2023-10-04 10:13:29,293 [1230] DEBUG pulse.iterate: Try new control
2023-10-04 10:13:29,294 [1230] DEBUG pulse.iterate: Current control: 0.020
2023-10-04 10:13:31,062 [1230] DEBUG pulse.iterate:
SUCCESFULL STEP:
2023-10-04 10:13:31,063 [1230] DEBUG pulse.iterate: Check target reached: NO
2023-10-04 10:13:31,064 [1230] DEBUG pulse.iterate: Maximum difference: 8.000e-02
2023-10-04 10:13:31,065 [1230] DEBUG pulse.iterate: Adapt step size. New step size: 0.015
2023-10-04 10:13:31,066 [1230] DEBUG pulse.iterate: Check target reached: NO
2023-10-04 10:13:31,066 [1230] DEBUG pulse.iterate: Maximum difference: 8.000e-02
2023-10-04 10:13:31,067 [1230] DEBUG pulse.iterate: Try new control
2023-10-04 10:13:31,068 [1230] DEBUG pulse.iterate: Current control: 0.035
2023-10-04 10:13:32,848 [1230] DEBUG pulse.iterate:
SUCCESFULL STEP:
2023-10-04 10:13:32,849 [1230] DEBUG pulse.iterate: Check target reached: NO
2023-10-04 10:13:32,850 [1230] DEBUG pulse.iterate: Maximum difference: 6.500e-02
2023-10-04 10:13:32,850 [1230] DEBUG pulse.iterate: Adapt step size. New step size: 0.022
2023-10-04 10:13:32,851 [1230] DEBUG pulse.iterate: Check target reached: NO
2023-10-04 10:13:32,852 [1230] DEBUG pulse.iterate: Maximum difference: 6.500e-02
2023-10-04 10:13:32,853 [1230] DEBUG pulse.iterate: Try new control
2023-10-04 10:13:32,853 [1230] DEBUG pulse.iterate: Current control: 0.058
2023-10-04 10:13:34,989 [1230] DEBUG pulse.iterate:
SUCCESFULL STEP:
2023-10-04 10:13:34,990 [1230] DEBUG pulse.iterate: Check target reached: NO
2023-10-04 10:13:34,991 [1230] DEBUG pulse.iterate: Maximum difference: 4.250e-02
2023-10-04 10:13:34,992 [1230] DEBUG pulse.iterate: Adapt step size. New step size: 0.034
2023-10-04 10:13:34,993 [1230] DEBUG pulse.iterate: Check target reached: NO
2023-10-04 10:13:34,994 [1230] DEBUG pulse.iterate: Maximum difference: 4.250e-02
2023-10-04 10:13:34,994 [1230] DEBUG pulse.iterate: Try new control
2023-10-04 10:13:34,995 [1230] DEBUG pulse.iterate: Current control: 0.091
2023-10-04 10:13:37,126 [1230] DEBUG pulse.iterate:
SUCCESFULL STEP:
2023-10-04 10:13:37,127 [1230] DEBUG pulse.iterate: Check target reached: NO
2023-10-04 10:13:37,128 [1230] DEBUG pulse.iterate: Maximum difference: 8.750e-03
2023-10-04 10:13:37,129 [1230] DEBUG pulse.iterate: Adapt step size. New step size: 0.051
2023-10-04 10:13:37,130 [1230] DEBUG pulse.iterate: Check target reached: NO
2023-10-04 10:13:37,131 [1230] DEBUG pulse.iterate: Maximum difference: 8.750e-03
2023-10-04 10:13:37,131 [1230] DEBUG pulse.iterate: Change step size for final iteration
2023-10-04 10:13:37,132 [1230] DEBUG pulse.iterate: Try new control
2023-10-04 10:13:37,133 [1230] DEBUG pulse.iterate: Current control: 0.100
2023-10-04 10:13:38,207 [1230] DEBUG pulse.iterate:
SUCCESFULL STEP:
2023-10-04 10:13:38,208 [1230] DEBUG pulse.iterate: Check target reached: YES!
2023-10-04 10:13:38,209 [1230] DEBUG pulse.iterate: Check target reached: YES!
([Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 47),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 175),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 224),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 273),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 330),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 387),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 420)],
[Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 45),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 173),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 222),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 271),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 328),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 385),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 418)])
# Get displacement and hydrostatic pressure
u, p = problem.state.split(deepcopy=True)
V = dolfin.VectorFunctionSpace(mesh, "CG", 1)
u_int = interpolate(u, V)
new_mesh = Mesh(mesh)
dolfin.ALE.move(new_mesh, u_int)
fig = plot(mesh, show=False)
fig.add_plot(plot(new_mesh, color="red", show=False))
fig.show()